Composition and temperature dependence of the crystal structure of Ni Mn Ga alloys

JOURNAL OF APPLIED PHYSICS VOLUME 95, NUMBER 12 15 JUNE 2004 Composition and temperature dependence of the crystal structure of Ni Mn Ga alloys N. Lanska a) Helsinki University of Technology, Laboratory of Biomedical Engineering, P.O. Box 2200, FIN-02015 HUT, Finland and Helsinki University of Technology, Laboratory of Physical Metallurgy and Materials Science, P.O. Box 6200, FIN-02015 HUT, Finland O. Söderberg, A. Sozinov, and Y. Ge Helsinki University of Technology, Laboratory of Physical Metallurgy and Materials Science, P.O. Box 6200, FIN-02015 HUT, Finland K. Ullakko Helsinki University of Technology, Laboratory of Biomedical Engineering, P.O. Box 2200, FIN-02015 HUT, Finland V. K. Lindroos Helsinki University of Technology, Laboratory of Physical Metallurgy and Materials Science, P.O. Box 6200, FIN-02015 HUT, Finland Received 2 December 2003; accepted 24 March 2004 The crystal structure of ferromagnetic near-stoichiometric Ni 2 MnGa alloys with different compositions has been studied at ambient temperature. The studied alloys, with five-layered 5M and seven-layered 7M martensitic phases, exhibit the martensitic transformation temperature (T M ) up to 353 K. Alloys with these crystal structures are the best candidates for magnetic-field-induced strain applications. The range of the average number of valence electrons per atom (e/a) was determined for phases 5M, 7M, and nonmodulated martensite. Furthermore, a correlation between the martensitic crystal structure, T M and e/a has been established. The lattice parameters ratio (c/a) as a function of e/a or T M has been obtained at ambient temperature for all martensitic phases. That the paramagnetic-ferromagnetic transition influences the structural phase transformation in the Ni Mn Ga system has been confirmed. 2004 American Institute of Physics. DOI: 10.1063/1.1748860 INTRODUCTION It was recently recognized that ferromagnetic Ni Mn Ga alloys with compositions near the stoichiometric Heusler composition Ni 2 MnGa are a class of smart materials showing a giant magnetic-field-induced strain MFIS. The mechanism of MFIS is based on the rearrangement of crystallographic domains twin variants in an applied magnetic field, which lowers magnetization energy. 1 This mechanism operates at temperatures below the Curie point (T C ) and martensitic transformation temperature (T M ). The behavior of the material in the magnetic field is determined by such material parameters as magnetocrystalline anisotropy (K U ), saturation magnetization, and mechanical stress necessary for twin variant rearrangement twinning stress. 2,3 During the last few years, the Ni Mn Ga system has been studied in detail experimentally and theoretically all over the world. It has been found that martensitic and magnetic phase transformation temperatures, 4 9 transformation enthalpy, 5,6 magnetocrystalline anisotropy, 8 and saturation magnetization 8,9 are highly composition dependent. To find the best alloys for practical applications, certain important properties of Ni Mn Ga have been mapped with their composition. 9,10 However, the effect of crystal structure on a Electronic mail: Nataliya.lanska@HUT.FI these properties still needs to be clarified in more detail. The crystal structure of martensite is an important factor that affects both the magnetic anisotropy and mechanical properties of ferromagnetic Ni Mn Ga alloys. 11 14 The lattice parameters a and c of the basic martensitic crystal structure in parent phase coordinates determine the maximal MFIS value described as 1 c/a. Almost all of the theoretical maximum values of MFIS have been obtained in fivelayered 5M and seven-layered 7M martensitic phases in the Ni Mn Ga system. 15,16 However, in the nonmodulated martensitic phase NM it has not been observed so far, despite the high magnetic anisotropy. 11 The reason for this is the high twinning stress in the NM phase, which was recently confirmed to be approximately 6 18 MPa. 14 Based on x-ray diffraction data, the unit cell of NM martensite has been determined to be non-modulated tetragonal with ratio c/a 1 in parent cubic phase coordinates. 17 It has been concluded that the crystal structure of 5M and 7M martensitic phases is more complex and that it can be described as the lattice modulated by periodic shuffling along (110) 110 p system or with a long-period stacking of 110 p close-packed planes. 17,18 Nevertheless, the basic unit cell of the 5M phase is often approximated to a tetragonal or monoclinic cell with ratio c/a 1 in parent cubic axes, while that of the 7M phase has been determined to be orthorhombic or monoclinic. 17 20 0021-8979/2004/95(12)/8074/5/$22.00 8074 2004 American Institute of Physics

J. Appl. Phys., Vol. 95, No. 12, 15 June 2004 Lanska et al. 8075 TABLE I. Chemical composition, martensitic transformation temperatures, Curie point, electron concentration, and type of martensitic phase at 298 K in studied alloys. Content at % M S M F A S A F T C e/a Phase Alloy Ni Mn Ga K K K K K 1 50.7 28.4 20.9 334 325 339 345 367 7.685 5M 2 50.7 28.3 21.0 330 323 338 343 363 7.681 5M 3 50.7 27.8 21.5 325 323 331 334 371 7.661 5M 4 50.6 28.5 20.9 333 331 339 341 371 7.682 5M 5 50.0 29.8 20.2 344 340 347 351 370 7.692 5M 6 50.0 28.9 21.1 321 311 320 330 374 7.656 5M 7 49.9 29.9 20.2 344 338 350 354 369 7.690 5M 8 49.7 29.1 21.2 311 309 319 321 372 7.643 5M 9 49.6 29.2 21.2 303 301 309 309 376 7.640 5M 10 49.2 30.6 20.2 328 323 333 337 370 7.668 5M 11 49.1 30.7 20.2 324 321 332 335 370 7.665 5M 12 49.0 30.3 20.7 312 309 318 323 370 7.642 5M 13 48.5 30.3 21.2 302 299 305 308 372 7.607 5M 14 51.0 28.5 20.5 356 350 354 360 365 7.710 7M 15 50.5 29.4 20.1 351 343 348 357 366 7.711 7M 16 49.5 30.3 20.2 341 337 344 348 363 7.677 7M 17 48.8 31.4 19.8 337 333 338 342 368 7.672 7M 18 54.9 23.8 21.3 559 541 568 587 360 7.795 NM 19 54.0 24.7 21.3 497 487 498 510 328 7.768 NM 20 53.9 24.4 21.7 530 524 551 560 336 7.749 NM 21 53.7 26.4 19.9 523 512 538 546 344 7.815 NM 22 53.3 24.6 22.1 465 459 468 476 371 7.715 NM 23 52.9 25.0 22.1 348 344 354 363 356 7.703 NM 24 52.8 25.7 21.5 390 367 377 404 382 7.724 NM 25 52.7 26.0 21.3 434 416 424 446 376 7.729 NM 26 52.4 25.6 22.0 423 414 424 434 375 7.692 NM 27 52.3 27.4 20.3 398 391 403 408 380 7.757 NM 28 51.7 27.7 20.6 383 369 381 394 386 7.726 NM 29 51.5 26.8 21.7 393 374 380 400 377 7.677 NM 30 51.2 27.4 21.4 371 366 371 375 370 7.68 NM 31 51.0 28.7 20.3 379 366 376 385 372 7.721 NM 32 50.5 30.4 19.1 391 376 383 397 378 7.751 NM 33 47.0 33.1 19.9 326 323 329 331 366 7.614 NM The crystal structure of the Ni Mn Ga martensitic phase strongly depends on composition and temperature. 5,18,21,22 The relationship between c/a and the average number of valence electrons per atom (e/a) has been investigated by Tsuchiya et al. 21 and Chernenko et al. 22 It is pointed out that e/a 7.7 corresponds to the crossing of lines T C versus e/a and T M versus e/a for Ni Mn Ga alloys. 22 This is a critical value, at which the crystal structure of the martensitic phase changes from 5M with c/a 1) to NM with c/a 1). This critical value was estimated by Tsuchiya et al. 21 to be e/a 7.61 7.62. However, in both publications, 21,22 the data concern mostly the NM phase, while the 7M martensitic phase was not studied and data for the 5M phase were restricted to the alloys with a martensitic phase transformation below ambient temperature. As mentioned above, only 5M and 7M structures exhibit MFIS. In the present work, the crystal structure of ferromagnetic near-stoichiometric Ni 2 MnGa alloys with different compositions in the electronic concentration range from e/a 7.60 to 7.82 is investigated. The present research is designed to find the alloy compositions with 5M or 7M structures having the highest possible martensitic transformation temperatures. EXPERIMENTAL PROCEDURES The studied Ni Mn Ga materials were manufactured at Outokumpu Research Oy and at AdaptaMat Ltd. After ho- FIG. 1. Ni and Mn content in the studied alloys. The marks correspond to the martensitic crystal structure observed at T 298 K. Straight lines indicate compositions with a constant average number of valence electron per atom e/a.

8076 J. Appl. Phys., Vol. 95, No. 12, 15 June 2004 Lanska et al. FIG. 2. c/a ratio for the alloys with NM phase at T 298 K as a function of the martensitic transformation temperature T M. FIG. 3. c/a ratio for the alloys with 5M phase at T 298 K as a function of the martensitic transformation temperature T M. FIG. 4. Monoclinic distortion for the alloys with 5M phase at T 298 K as a function of the martensitic transformation temperature T M. a Difference of parameters a and b, a-b and b deviation of the angle from 90, -90. mogenization at 1253 K for 48 h, and aging at 1073 K for 72 h, the ingots were cooled in air to room temperature. The samples with suitable sizes were cut from the ingots with a spark cutting machine. After cutting, the samples were at first wet polished and, finally, electropolished in 25% nitric acidethanol solution at a temperature of 273 K for 30 s with 12 V and 0.1 A/mm 2. The chemical compositions were determined by means of a scanning electron microscope equipped with an energy-dispersive spectrometer. Transformation temperatures M S, M F, A S, A F, and Curie point T C were measured using low field ac magnetic susceptibility 77 573 K and a differential scanning calorimeter Linkam 600 113 873 K. A Philips X Pert x-ray diffractometer equipped with an Eulerian cradle, Co-tube, and parallel beam optics x-ray lens and parallel plate collimator with a divergence 0.3 ) was used to study the martensitic structure. Texture type and 2 scans were used to find the main Bragg reflections. X Pert Graphics and Identify software was applied for the analysis of peaks. The lattice parameters of the basic crystal structure were determined in parent phase cubic coordinates, according to the main Bragg reflections. The existence of lattice modulation was confirmed by a linear scan in reciprocal space (Q-scan between the main peaks in 110 * direction. Here, the presence of the additional spots, and the number of the intervals into which they divide the distance between the main peaks, indicate lattice modulation and its periodicity. RESULTS AND DISCUSSION Near-stoichiometric Ni 2 MnGa alloys with different compositions, exhibiting martensitic transformation temperatures and a Curie temperature higher than 300 K, were chosen for crystal structure study. Consequently, it was possible to carry out x-ray investigation of the ferromagnetic martensitic crystal structures at ambient temperature. The valence electron concentration of the alloys lies in the range from e/a 7.60 to 7.82. For calculation of the value for e/a, the valence electrons per atom were 10 for Ni, 7 for Mn, and 3 for Ga. 5 The e/a values for the studied alloys are presented in Table I, together with the chemical composition, the transformation temperatures M S, M F, A S, A F, Curie temperature T C, and the martensite type 5M, 7M, and NM. In addition, Fig. 1 shows the Ni and Mn content of the alloys together with the type of martensitic structure observed at room temperature. In all the alloys with a martensitic transformation temperature T M above Curie point T C, the martensite was of the NM type. Here, T M (M S M F )/2, and M S and M F are the start and finish temperatures of the martensitic transformation. Among the alloys with NM martensite at room temperature, there are a few alloys alloys 23, 24, 28, 30, and 33, see Table I having T M T C. The electron concentration range for the alloys with a NM phase is from e/a 7.61 to 7.82, while their T M is in the wide temperature range of 323 550 K. We confirmed that the unit cell of the NM phase is tetragonal with c/a 1. No lattice modulation is observed for this phase. The dependence of c/a on T M for the alloys with a nonlayered martensitic phase is shown in Fig. 2. The presented data indicate that the lattice tetragonality approaches maximum c/a 1.23 at T M 550 K. The tetragonal distortion (c/a 1) decreases with a decreasing T M. The 5M phase is found in those alloys with 301 K T M 342 K in the electron concentration range from e/a

J. Appl. Phys., Vol. 95, No. 12, 15 June 2004 Lanska et al. 8077 FIG. 5. Scattering intensity distribution along the line between 400 and 620 nodes in reciprocal space for 5M phase alloy 9. Arrows mark the additional peaks connected with five-layered modulation of the lattice. 7.61 to 7.69. The Curie temperature for such alloys is higher than T M. The basic unit cell of these alloys is determined as monoclinic with c/a 1 and the maximum angle between a and b axes 90.50. The splitting of the main peaks due to monoclinic distortion of the 5M lattice was clearly observed at large 2 angles. In Fig. 3, c/a ratio of the alloys with a 5M phase is plotted as a function of T M. The decreasing of T M leads to the linear increasing of c/a and, consequently, to a decreasing of the maximal theoretical MFIS value described as 1 c/a. According to Fig. 4, the difference of the lattice parameters a and b, together with the deviation of the angle from 90, becomes smaller with decreasing T M. Monoclinic distortion of the lattice therefore decreases with a lowering T M. Five-layered modulation of these alloys is recognized as the four additional spots in the linear scan between 400 and 620 peaks in reciprocal space see Fig. 5. Only four of the studied alloys showed a 7M phase at room temperature. Their T M lies in the narrow temperature range of 335 353 K below T C, while their e/a is in the range of 7.67 7.71. The basic unit cell for these alloys was FIG. 7. c/a ratio at T 298 K as a function of martensitic transformation temperature (T M ) for the alloys with 5M, 7M, and NM phases. The boundaries in the inset show the temperature range in which all the phases were observed. found to be monoclinic with c/a 1 and angle 90.5. Although the unit cell of both 7M and 5M martensites is monoclinic, the difference between the lattice parameters a and b 0.038 0.040 nm in 7M martensite is considerably higher than that in 5M martensite. The ratio c/a for 7M martensite is lower than that for 5M martensite. It is approximately of the same value 0.890 0.894 in all studied alloys. The maximal theoretical MFIS value (1 c/a) for 7M martensite ( 0.11) is higher than for 5M martensite ( 0.07). Seven-layered modulation of these alloys has been recognized as the six additional spots in a linear scan between 400 and 620 peaks in reciprocal space Fig. 6. The summarized data of c/a versus T M for all martensitic phases are shown in Fig. 7. There is a specific range, 323 K T M 353 K, where alloys with different martensitic phases are simultaneously observed. This same region is present in Fig. 8, in which c/a is shown as a function of e/a for all martensitic phases. Now the multiphase region of e/a is limited with values 7.61 and 7.71. The change from c/a 1 toc/a 1 takes place within this whole area instead of FIG. 6. Scattering intensity distribution along the line between 400 and 620 nodes in reciprocal space for 7M phase alloy 17. Arrows mark the additional peaks connected with seven-layered modulation of the lattice. FIG. 8. c/a ratio at T 298 K as a function of electron concentration e/a for the alloys with 5M, 7M, and NM phases. The boundaries show the e/a range in which all the phases were observed.

8078 J. Appl. Phys., Vol. 95, No. 12, 15 June 2004 Lanska et al. at one sharp boundary. The first limiting value e/a 7.61 is in close agreement with the value determined by Tsuchiya et al., 21 while the second e/a 7.71 is close to the value determined by Chernenko et al. 22 Probably, the closeness of martensitic and ferromagnetic transitions in this range introduces uncertainty to the formation of the structure type resulting from austenite-martensite transformation. In this region, as there is no one-to-one correspondence between crystal structure and a single variable such as T M or the average number of valence electron per atom e/a, the relation between alloy components should be taken into account. Particularly in the studied set of the alloys, at the same value e/a, increasing the Ni content to above 51 at. % leads to nonlayered, rather than 5M or 7M, structure formation see Figs. 1 and 8. It should be noticed that the present work is concentrating on the alloys with pure martensitic phases even though the alloys with mixed phases were also observed in the electronic concentration range of 7.61 7.71. Their structure consists of a mixture of 5M and 7M phases or 7M and NM phases, but it was never observed as a combination of 5M and NM phases. According to the present data, for e/a 7.71 or T M 353 K, only the NM phase exists, while layered phases 5M and 7M were observed at lower values of e/a and T M. CONCLUSIONS The correlation between the crystal structure, composition and the martensitic transformation temperature T M was investigated in near-stoichiometric Ni 2 MnGa alloys with T M above ambient temperatures. Based on the investigations of the present study the following conclusions can be drawn: 1 Ni Mn Ga ferromagnetic alloys having T M up to 353 K and a modulated martensitic crystal structure 5M or 7M were found. They are good candidates for practical applications of magnetic shape memory materials. 2 The influence of paramagnetic-ferromagnetic phase transformation on the structural phase transformation in the Ni Mn Ga system was confirmed. First, if T M is higher than T C, only the nonmodulated tetragonal crystal structure NM was observed. Second, cubic-5m and cubic-7m martensitic transformations were observed only in the alloys with T M below T C. 3 For the alloys having T M in the temperature range from 323 to 353 K 10 50 K below the Curie point, there is no one-to-one correspondence between crystal structure and single variables such as T M or the average number of valence electron per atom e/a. Particularly in the e/a range from 7.61 to 7.72, different crystal structures 5M, 7M, or NM were observed as a result of martensitic transformation. 4 The tetragonal distortion of the lattice in the NM phase as well as monoclinic distortion in the 5M phase decreases with decreasing T M. ACKNOWLEDGMENTS The authors would like to acknowledge the funding support given by the National Technology Agency of Finland Tekes as well as that from their industrial research partners Nokia Research Center, Outokumpu Research Oy, Metso Oyj, and AdaptaMat Ltd. and ONR Project No. N00014-02- 1-0462. Furthermore, the help of Dr. Xuwen Liu is gratefully acknowledged. 1 K. Ullakko, J. K. Huang, C. Kantner, R. C. O Handley, and V. V. Kokorin, Appl. Phys. Lett. 69, 1966 1996. 2 R. C. O Handley, J. Appl. Phys. 83, 3263 1998. 3 A. A. Likhachev, A. Sozinov, and K. Ullakko, Proc. SPIE 4333, 197 2001. 4 A. N. Vasil ev, A. D. Bozhko, V. V. Khovailo, I. E. Dikshtein, V. G. Shavrov, V. D. Buchelnicov, M. Matsumoto, S. Suzuki, T. Takagi, and J. Tani, Phys. Rev. B 59, 1113 1999. 5 V. A. Chernenko, Scr. Mater. 40, 523 1999. 6 S. K. Wu and S. T. Yang, Mater. Lett. 57, 4291 2003. 7 C. Jiang, G. Feng, S. Shengkai, and H. Xu, Mater. Sci. Eng., A 342, 231 2003. 8 F. Albertini, L. Pareti, A. Paoluzi, L. 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